Dynamics of $\mathrm{SL}_2(\mathbb{R})$ over moduli space in genus two

Abstract

This paper classifies orbit closures and invariant measures for the natural action of $\operatorname{SL}_2(\mathbb{R})$ on $\Omega \mathcal{M}_2$, the bundle of holomorphic 1-forms over the moduli space of Riemann surfaces of genus two.

Authors

Curtis T. McMullen

Department of Mathematics
Harvard University
Cambridge, MA 02138
United States